“Is there a way to improve

“Is there a way to improve the quality without the user having to click the HD option?”

Not that I know of. Youtube sacrifices image quality for the ability to watch videos with little loading times.

Do you have any experience with paid 3rd party video hosting sites – where I can upload high quality and embed them in my site?

I’m a big fan of http://www.exposureroom.com and use them often to embed videos to my Filmmaker Myspace.